{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Implicit Compact Pade (ICP) Scheme\n",
    "\n",
    "Equation 22:\n",
    "\n",
    "$$\\frac{1}{\\alpha}\\left( \\frac{1}{12}\\frac{\\partial u}{\\partial t}\\Bigr|_{i-1} + \\frac{10}{12}\\frac{\\partial u}{\\partial t}\\Bigr|_{i} + \\frac{1}{12}\\frac{\\partial u}{\\partial t}\\Bigr|_{i+1} \\right) = \\frac{u_{i-1} - 2u_i + u_{i+1}}{\\Delta x^2}$$\n",
    "\n",
    "Equation 23:\n",
    "\n",
    "$$\\frac{1}{\\alpha}\\left( \\frac{u_{i-1}^{n+1} - u_{i-1}^{n}}{12\\Delta t} + 10\\frac{u_{i}^{n+1} - u_{i}^{n}}{12\\Delta t} + \\frac{u_{i+1}^{n+1} - u_{i+1}^{n}}{12\\Delta t} \\right) = \\frac{u_{i-1}^{n+1} - 2u_{i}^{n+1} + u_{i+1}^{n+1} + u_{i-1}^{n} - 2u_{i}^{n} + u_{i+1}^{n}}{2\\Delta x^2}$$\n",
    "\n",
    "Equation 28:\n",
    "\n",
    "$$r_i = \\frac{-2}{\\alpha\\Delta t}\\left( u_{i-1}^{(n)} + 10u_{i}^{(n)} + u_{i+1}^{(n)} \\right) - \\frac{12}{\\Delta x^2}\\left( u_{i-1}^{(n)} - 2u_{i}^{(n)} + u_{i+1}^{(n)} \\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_l, x_r, t = -1, 1, 1\n",
    "dx, dt = 0.025, 0.0025\n",
    "nx = int((x_r - x_l) / dx)\n",
    "nt = int(t / dt)\n",
    "\n",
    "alpha = 1 / np.pi**2\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "x = np.linspace(x_l, x_r, nx+1)\n",
    "\n",
    "u[0, :] = -np.sin(np.pi*x, dtype=np.double)\n",
    "u[0, 0], u[0, -1] = 0, 0\n",
    "\n",
    "a = [12.0 / dx**2 - 2.0 / (alpha * dt)] * (nx-1) + [0]\n",
    "b = [1] + [-24.0 / dx**2 - 20.0 / (alpha * dt)] * (nx-1) + [1]\n",
    "c = [0] + [12.0 / dx**2 - 2.0 / (alpha * dt)] * (nx-1)\n",
    "for i in range(1, nt+1):\n",
    "    d = [0] + [-2 / (alpha * dt) * (u[i-1, j+1] + 10 * u[i-1, j] + u[i-1, j-1]) - 12 / dx**2 * (u[i-1, j+1] - 2 * u[i-1, j] + u[i-1, j-1]) for j in range(1, nx)] + [0]\n",
    "    A = np.diag(b,0) + np.diag(a,-1) + np.diag(c,1)\n",
    "    u[i, :] = np.linalg.solve(A, d)\n",
    "u_ref = -np.exp(-t) * np.sin(np.pi * x)\n",
    "error = np.abs(u_ref - u[-1, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4), dpi=100)\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x, u_ref, \"k-\", linewidth=1.0, label=\"Solution\")\n",
    "plt.scatter(x, u[-1, :], facecolor=\"none\", edgecolor=\"blue\", s=20, linewidths=0.5, label=\"ICP\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$u$\")\n",
    "plt.title(\"Solution field\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x, error, facecolor=\"none\", edgecolor=\"red\", s=20, linewidths=0.5)\n",
    "plt.ylabel(r\"$\\epsilon$\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.title(\"Discretization error\")\n",
    "plt.tight_layout()\n",
    "plt.ticklabel_format(axis='y', style='sci', scilimits=(-7,-7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gpytorch",
   "language": "python",
   "name": "gpytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
